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<div class="title">TensorFFT.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2015 Jianwei Cui &lt;thucjw@gmail.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_CXX11_TENSOR_TENSOR_FFT_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_CXX11_TENSOR_TENSOR_FFT_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">bool</span> NeedUprade&gt; <span class="keyword">struct </span>MakeComplex {</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  T operator() (<span class="keyword">const</span> T&amp; val)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> val; }</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;};</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160; </div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="keyword">template</span> &lt;&gt; <span class="keyword">struct </span>MakeComplex&lt;true&gt; {</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  std::complex&lt;T&gt; operator() (<span class="keyword">const</span> T&amp; val)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> std::complex&lt;T&gt;(val, 0); }</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;};</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160; </div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="keyword">template</span> &lt;&gt; <span class="keyword">struct </span>MakeComplex&lt;false&gt; {</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;  std::complex&lt;T&gt; operator() (<span class="keyword">const</span> std::complex&lt;T&gt;&amp; val)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> val; }</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;};</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160; </div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> ResultType&gt; <span class="keyword">struct </span>PartOf {</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt; T operator() (<span class="keyword">const</span> T&amp; val)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> val; }</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;};</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160; </div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="keyword">template</span> &lt;&gt; <span class="keyword">struct </span>PartOf&lt;RealPart&gt; {</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt; T operator() (<span class="keyword">const</span> std::complex&lt;T&gt;&amp; val)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> val.real(); }</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;};</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="keyword">template</span> &lt;&gt; <span class="keyword">struct </span>PartOf&lt;ImagPart&gt; {</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt; T operator() (<span class="keyword">const</span> std::complex&lt;T&gt;&amp; val)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> val.imag(); }</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;};</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160; </div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> FFT, <span class="keyword">typename</span> XprType, <span class="keywordtype">int</span> FFTResultType, <span class="keywordtype">int</span> FFTDir&gt;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="keyword">struct </span>traits&lt;TensorFFTOp&lt;FFT, XprType, FFTResultType, FFTDir&gt; &gt; : <span class="keyword">public</span> traits&lt;XprType&gt; {</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <span class="keyword">typedef</span> traits&lt;XprType&gt; XprTraits;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits&lt;typename XprTraits::Scalar&gt;::Real RealScalar;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> std::complex&lt;RealScalar&gt; ComplexScalar;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> XprTraits::Scalar InputScalar;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar&gt; OutputScalar;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> XprTraits::StorageKind StorageKind;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> XprTraits::Index <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> XprType::Nested Nested;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  <span class="keyword">typedef</span> std::remove_reference_t&lt;Nested&gt; Nested_;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  <span class="keyword">static</span> constexpr <span class="keywordtype">int</span> NumDimensions = XprTraits::NumDimensions;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  <span class="keyword">static</span> constexpr <span class="keywordtype">int</span> Layout = XprTraits::Layout;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> traits&lt;XprType&gt;::PointerType PointerType;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;};</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160; </div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> FFT, <span class="keyword">typename</span> XprType, <span class="keywordtype">int</span> FFTResultType, <span class="keywordtype">int</span> FFTDirection&gt;</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="keyword">struct </span>eval&lt;TensorFFTOp&lt;FFT, XprType, FFTResultType, FFTDirection&gt;, <a class="code" href="namespaceEigen.html">Eigen</a>::Dense&gt; {</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">const</span> TensorFFTOp&lt;FFT, XprType, FFTResultType, FFTDirection&gt;&amp; type;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;};</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160; </div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> FFT, <span class="keyword">typename</span> XprType, <span class="keywordtype">int</span> FFTResultType, <span class="keywordtype">int</span> FFTDirection&gt;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;<span class="keyword">struct </span>nested&lt;TensorFFTOp&lt;FFT, XprType, FFTResultType, FFTDirection&gt;, 1, typename eval&lt;TensorFFTOp&lt;FFT, XprType, FFTResultType, FFTDirection&gt; &gt;::type&gt; {</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  <span class="keyword">typedef</span> TensorFFTOp&lt;FFT, XprType, FFTResultType, FFTDirection&gt; type;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;};</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160; </div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;}  <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> FFT, <span class="keyword">typename</span> XprType, <span class="keywordtype">int</span> FFTResultType, <span class="keywordtype">int</span> FFTDir&gt;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="keyword">class </span>TensorFFTOp : <span class="keyword">public</span> TensorBase&lt;TensorFFTOp&lt;FFT, XprType, FFTResultType, FFTDir&gt;, ReadOnlyAccessors&gt; {</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Eigen::internal::traits&lt;TensorFFTOp&gt;::Scalar Scalar;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">Eigen::NumTraits&lt;Scalar&gt;::Real</a> RealScalar;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> std::complex&lt;RealScalar&gt; ComplexScalar;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar&gt; OutputScalar;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  <span class="keyword">typedef</span> OutputScalar CoeffReturnType;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Eigen::internal::nested&lt;TensorFFTOp&gt;::type Nested;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Eigen::internal::traits&lt;TensorFFTOp&gt;::StorageKind StorageKind;</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Eigen::internal::traits&lt;TensorFFTOp&gt;::Index <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160; </div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorFFTOp(<span class="keyword">const</span> XprType&amp; expr, <span class="keyword">const</span> FFT&amp; fft)</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;      : m_xpr(expr), m_fft(fft) {}</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160; </div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;  <span class="keyword">const</span> FFT&amp; fft()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_fft; }</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160; </div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  <span class="keyword">const</span> internal::remove_all_t&lt;typename XprType::Nested&gt;&amp; expression()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    <span class="keywordflow">return</span> m_xpr;</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  }</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160; </div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="keyword">typename</span> XprType::Nested m_xpr;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  <span class="keyword">const</span> FFT m_fft;</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;};</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;<span class="comment">// Eval as rvalue</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> FFT, <span class="keyword">typename</span> ArgType, <span class="keyword">typename</span> Device, <span class="keywordtype">int</span> FFTResultType, <span class="keywordtype">int</span> FFTDir&gt;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;<span class="keyword">struct </span>TensorEvaluator&lt;const TensorFFTOp&lt;FFT, ArgType, FFTResultType, FFTDir&gt;, Device&gt; {</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  <span class="keyword">typedef</span> TensorFFTOp&lt;FFT, ArgType, FFTResultType, FFTDir&gt; XprType;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> XprType::Index Index;</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  <span class="keyword">static</span> constexpr <span class="keywordtype">int</span> NumDims = internal::array_size&lt;typename TensorEvaluator&lt;ArgType, Device&gt;::Dimensions&gt;::value;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  <span class="keyword">typedef</span> DSizes&lt;Index, NumDims&gt; Dimensions;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> XprType::Scalar Scalar;</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">Eigen::NumTraits&lt;Scalar&gt;::Real</a> RealScalar;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> std::complex&lt;RealScalar&gt; ComplexScalar;</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> TensorEvaluator&lt;ArgType, Device&gt;::Dimensions InputDimensions;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  <span class="keyword">typedef</span> internal::traits&lt;XprType&gt; XprTraits;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> XprTraits::Scalar InputScalar;</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;FFTResultType == RealPart || FFTResultType == ImagPart, RealScalar, ComplexScalar&gt; OutputScalar;</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  <span class="keyword">typedef</span> OutputScalar CoeffReturnType;</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> PacketType&lt;OutputScalar, Device&gt;::type PacketReturnType;</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  <span class="keyword">static</span> constexpr <span class="keywordtype">int</span> PacketSize = internal::unpacket_traits&lt;PacketReturnType&gt;::size;</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  <span class="keyword">typedef</span> StorageMemory&lt;CoeffReturnType, Device&gt; Storage;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Storage::Type EvaluatorPointerType;</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160; </div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;  <span class="keyword">static</span> constexpr <span class="keywordtype">int</span> Layout = TensorEvaluator&lt;ArgType, Device&gt;::Layout;</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    IsAligned = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    PacketAccess = <span class="keyword">true</span>,</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    BlockAccess = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    PreferBlockAccess = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    CoordAccess = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    RawAccess = <span class="keyword">false</span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;  };</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160; </div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  <span class="comment">//===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//</span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;  <span class="keyword">typedef</span> internal::TensorBlockNotImplemented TensorBlock;</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  <span class="comment">//===--------------------------------------------------------------------===//</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160; </div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;  EIGEN_STRONG_INLINE TensorEvaluator(<span class="keyword">const</span> XprType&amp; op, <span class="keyword">const</span> Device&amp; device) : m_fft(op.fft()), m_impl(op.expression(), device), m_data(NULL), m_device(device) {</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keyword">const</span> <span class="keyword">typename</span> TensorEvaluator&lt;ArgType, Device&gt;::Dimensions&amp; input_dims = m_impl.dimensions();</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; NumDims; ++i) {</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;      eigen_assert(input_dims[i] &gt; 0);</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;      m_dimensions[i] = input_dims[i];</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    }</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160; </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    <span class="keywordflow">if</span> (<span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(Layout) == <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="codeRef" href="../group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a>)) {</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;      m_strides[0] = 1;</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; NumDims; ++i) {</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;        m_strides[i] = m_strides[i - 1] * m_dimensions[i - 1];</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;      }</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;    } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;      m_strides[NumDims - 1] = 1;</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = NumDims - 2; i &gt;= 0; --i) {</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;        m_strides[i] = m_strides[i + 1] * m_dimensions[i + 1];</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;      }</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    }</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    m_size = m_dimensions.TotalSize();</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  }</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160; </div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">const</span> Dimensions&amp; dimensions()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;    <span class="keywordflow">return</span> m_dimensions;</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;  }</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160; </div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;  EIGEN_STRONG_INLINE <span class="keywordtype">bool</span> evalSubExprsIfNeeded(EvaluatorPointerType data) {</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    m_impl.evalSubExprsIfNeeded(NULL);</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    <span class="keywordflow">if</span> (data) {</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;      evalToBuf(data);</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;      <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;      m_data = (EvaluatorPointerType)m_device.get((CoeffReturnType*)(m_device.allocate_temp(<span class="keyword">sizeof</span>(CoeffReturnType) * m_size)));</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;      evalToBuf(m_data);</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;      <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    }</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  }</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160; </div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  EIGEN_STRONG_INLINE <span class="keywordtype">void</span> cleanup() {</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    <span class="keywordflow">if</span> (m_data) {</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;      m_device.deallocate(m_data);</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;      m_data = NULL;</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    }</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    m_impl.cleanup();</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;  }</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160; </div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE CoeffReturnType coeff(Index index)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    <span class="keywordflow">return</span> m_data[index];</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  }</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160; </div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  <span class="keyword">template</span> &lt;<span class="keywordtype">int</span> LoadMode&gt;</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE PacketReturnType</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  packet(Index index)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    <span class="keywordflow">return</span> internal::ploadt&lt;PacketReturnType, LoadMode&gt;(m_data + index);</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  }</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160; </div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;  costPerCoeff(<span class="keywordtype">bool</span> vectorized)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    <span class="keywordflow">return</span> TensorOpCost(<span class="keyword">sizeof</span>(CoeffReturnType), 0, 0, vectorized, PacketSize);</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  }</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160; </div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  EIGEN_DEVICE_FUNC EvaluatorPointerType data()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_data; }</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;<span class="preprocessor">#ifdef EIGEN_USE_SYCL</span></div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  <span class="comment">// binding placeholder accessors to a command group handler for SYCL</span></div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> bind(cl::sycl::handler &amp;cgh)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;    m_data.bind(cgh);</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  }</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160; </div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160; <span class="keyword">private</span>:</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> evalToBuf(EvaluatorPointerType data) {</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">bool</span> write_to_out = internal::is_same&lt;OutputScalar, ComplexScalar&gt;::value;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    ComplexScalar* buf = write_to_out ? (ComplexScalar*)data : (ComplexScalar*)m_device.allocate(<span class="keyword">sizeof</span>(ComplexScalar) * m_size);</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160; </div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    <span class="keywordflow">for</span> (Index i = 0; i &lt; m_size; ++i) {</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;      buf[i] = MakeComplex&lt;internal::is_same&lt;InputScalar, RealScalar&gt;::value&gt;()(m_impl.coeff(i));</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    }</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160; </div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; m_fft.size(); ++i) {</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;      <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> dim = m_fft[i];</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;      eigen_assert(dim &gt;= 0 &amp;&amp; dim &lt; NumDims);</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;      <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> line_len = m_dimensions[dim];</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;      eigen_assert(line_len &gt;= 1);</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;      ComplexScalar* line_buf = (ComplexScalar*)m_device.allocate(<span class="keyword">sizeof</span>(ComplexScalar) * line_len);</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;      <span class="keyword">const</span> <span class="keywordtype">bool</span> is_power_of_two = isPowerOfTwo(line_len);</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;      <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> good_composite = is_power_of_two ? 0 : findGoodComposite(line_len);</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;      <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> log_len = is_power_of_two ? getLog2(line_len) : getLog2(good_composite);</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160; </div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;      ComplexScalar* a = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(<span class="keyword">sizeof</span>(ComplexScalar) * good_composite);</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;      ComplexScalar* b = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(<span class="keyword">sizeof</span>(ComplexScalar) * good_composite);</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;      ComplexScalar* pos_j_base_powered = is_power_of_two ? NULL : (ComplexScalar*)m_device.allocate(<span class="keyword">sizeof</span>(ComplexScalar) * (line_len + 1));</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;      <span class="keywordflow">if</span> (!is_power_of_two) {</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;        <span class="comment">// Compute twiddle factors</span></div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;        <span class="comment">//   t_n = exp(sqrt(-1) * pi * n^2 / line_len)</span></div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;        <span class="comment">// for n = 0, 1,..., line_len-1.</span></div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;        <span class="comment">// For n &gt; 2 we use the recurrence t_n = t_{n-1}^2 / t_{n-2} * t_1^2</span></div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160; </div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;        <span class="comment">// The recurrence is correct in exact arithmetic, but causes</span></div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;        <span class="comment">// numerical issues for large transforms, especially in</span></div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;        <span class="comment">// single-precision floating point.</span></div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;        <span class="comment">//</span></div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;        <span class="comment">// pos_j_base_powered[0] = ComplexScalar(1, 0);</span></div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;        <span class="comment">// if (line_len &gt; 1) {</span></div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;        <span class="comment">//   const ComplexScalar pos_j_base = ComplexScalar(</span></div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;        <span class="comment">//       numext::cos(M_PI / line_len), numext::sin(M_PI / line_len));</span></div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;        <span class="comment">//   pos_j_base_powered[1] = pos_j_base;</span></div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;        <span class="comment">//   if (line_len &gt; 2) {</span></div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;        <span class="comment">//     const ComplexScalar pos_j_base_sq = pos_j_base * pos_j_base;</span></div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;        <span class="comment">//     for (int i = 2; i &lt; line_len + 1; ++i) {</span></div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;        <span class="comment">//       pos_j_base_powered[i] = pos_j_base_powered[i - 1] *</span></div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;        <span class="comment">//           pos_j_base_powered[i - 1] /</span></div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;        <span class="comment">//           pos_j_base_powered[i - 2] *</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;        <span class="comment">//           pos_j_base_sq;</span></div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;        <span class="comment">//     }</span></div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;        <span class="comment">//   }</span></div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;        <span class="comment">// }</span></div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;        <span class="comment">// TODO(rmlarsen): Find a way to use Eigen&#39;s vectorized sin</span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;        <span class="comment">// and cosine functions here.</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; line_len + 1; ++j) {</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;          <span class="keywordtype">double</span> <a class="codeRef" href="../namespaceEigen.html#aa539408a09481d35961e11ee78793db1">arg</a> = ((EIGEN_PI * j) * j) / line_len;</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;          std::complex&lt;double&gt; tmp(numext::cos(<a class="codeRef" href="../namespaceEigen.html#aa539408a09481d35961e11ee78793db1">arg</a>), numext::sin(<a class="codeRef" href="../namespaceEigen.html#aa539408a09481d35961e11ee78793db1">arg</a>));</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;          pos_j_base_powered[j] = <span class="keyword">static_cast&lt;</span>ComplexScalar<span class="keyword">&gt;</span>(tmp);</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;        }</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;      }</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160; </div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;      <span class="keywordflow">for</span> (Index partial_index = 0; partial_index &lt; m_size / line_len; ++partial_index) {</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> base_offset = getBaseOffsetFromIndex(partial_index, dim);</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160; </div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;        <span class="comment">// get data into line_buf</span></div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> stride = m_strides[dim];</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;        <span class="keywordflow">if</span> (stride == 1) {</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;          m_device.memcpy(line_buf, &amp;buf[base_offset], line_len*<span class="keyword">sizeof</span>(ComplexScalar));</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;        } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;          <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> offset = base_offset;</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;          <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; line_len; ++j, offset += stride) {</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;            line_buf[j] = buf[offset];</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;          }</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;        }</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160; </div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;        <span class="comment">// process the line</span></div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;        <span class="keywordflow">if</span> (is_power_of_two) {</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;          processDataLineCooleyTukey(line_buf, line_len, log_len);</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;        }</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;        <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;          processDataLineBluestein(line_buf, line_len, good_composite, log_len, a, b, pos_j_base_powered);</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;        }</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160; </div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;        <span class="comment">// write back</span></div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;        <span class="keywordflow">if</span> (FFTDir == FFT_FORWARD &amp;&amp; stride == 1) {</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;          m_device.memcpy(&amp;buf[base_offset], line_buf, line_len*<span class="keyword">sizeof</span>(ComplexScalar));</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;        } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;          <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> offset = base_offset;</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;          <span class="keyword">const</span> ComplexScalar div_factor =  ComplexScalar(1.0 / line_len, 0);</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;          <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; line_len; ++j, offset += stride) {</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;             buf[offset] = (FFTDir == FFT_FORWARD) ? line_buf[j] : line_buf[j] * div_factor;</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;          }</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;        }</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;      }</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;      m_device.deallocate(line_buf);</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;      <span class="keywordflow">if</span> (!is_power_of_two) {</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;        m_device.deallocate(a);</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;        m_device.deallocate(b);</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;        m_device.deallocate(pos_j_base_powered);</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;      }</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    }</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160; </div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;    <span class="keywordflow">if</span>(!write_to_out) {</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;      <span class="keywordflow">for</span> (Index i = 0; i &lt; m_size; ++i) {</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;        data[i] = PartOf&lt;FFTResultType&gt;()(buf[i]);</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;      }</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;      m_device.deallocate(buf);</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    }</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;  }</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160; </div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">static</span> <span class="keywordtype">bool</span> isPowerOfTwo(Index x) {</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;    eigen_assert(x &gt; 0);</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;    <span class="keywordflow">return</span> !(x &amp; (x - 1));</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;  }</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160; </div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;  <span class="comment">// The composite number for padding, used in Bluestein&#39;s FFT algorithm</span></div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">static</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> findGoodComposite(Index n) {</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 2;</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;    <span class="keywordflow">while</span> (i &lt; 2 * n - 1) i *= 2;</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;    <span class="keywordflow">return</span> i;</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  }</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160; </div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">static</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> getLog2(Index m) {</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> log2m = 0;</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;    <span class="keywordflow">while</span> (m &gt;&gt;= 1) log2m++;</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;    <span class="keywordflow">return</span> log2m;</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;  }</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160; </div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;  <span class="comment">// Call Cooley Tukey algorithm directly, data length must be power of 2</span></div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> processDataLineCooleyTukey(ComplexScalar* line_buf, Index line_len, Index log_len) {</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;    eigen_assert(isPowerOfTwo(line_len));</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;    scramble_FFT(line_buf, line_len);</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;    compute_1D_Butterfly&lt;FFTDir&gt;(line_buf, line_len, log_len);</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;  }</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160; </div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  <span class="comment">// Call Bluestein&#39;s FFT algorithm, m is a good composite number greater than (2 * n - 1), used as the padding length</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> processDataLineBluestein(ComplexScalar* line_buf, Index line_len, Index good_composite, Index log_len, ComplexScalar* a, ComplexScalar* b, <span class="keyword">const</span> ComplexScalar* pos_j_base_powered) {</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = line_len;</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = good_composite;</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;    ComplexScalar* data = line_buf;</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160; </div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;    <span class="keywordflow">for</span> (Index i = 0; i &lt; n; ++i) {</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;      <span class="keywordflow">if</span>(FFTDir == FFT_FORWARD) {</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;        a[i] = data[i] * numext::conj(pos_j_base_powered[i]);</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;      }</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;      <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;        a[i] = data[i] * pos_j_base_powered[i];</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;      }</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;    }</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    <span class="keywordflow">for</span> (Index i = n; i &lt; m; ++i) {</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;      a[i] = ComplexScalar(0, 0);</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    }</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160; </div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    <span class="keywordflow">for</span> (Index i = 0; i &lt; n; ++i) {</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;      <span class="keywordflow">if</span>(FFTDir == FFT_FORWARD) {</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;        b[i] = pos_j_base_powered[i];</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;      }</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;      <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;        b[i] = numext::conj(pos_j_base_powered[i]);</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;      }</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;    }</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;    <span class="keywordflow">for</span> (Index i = n; i &lt; m - n; ++i) {</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;      b[i] = ComplexScalar(0, 0);</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;    }</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;    <span class="keywordflow">for</span> (Index i = m - n; i &lt; m; ++i) {</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;      <span class="keywordflow">if</span>(FFTDir == FFT_FORWARD) {</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;        b[i] = pos_j_base_powered[m-i];</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;      }</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;      <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;        b[i] = numext::conj(pos_j_base_powered[m-i]);</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;      }</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    }</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160; </div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    scramble_FFT(a, m);</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    compute_1D_Butterfly&lt;FFT_FORWARD&gt;(a, m, log_len);</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160; </div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    scramble_FFT(b, m);</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;    compute_1D_Butterfly&lt;FFT_FORWARD&gt;(b, m, log_len);</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160; </div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    <span class="keywordflow">for</span> (Index i = 0; i &lt; m; ++i) {</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;      a[i] *= b[i];</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    }</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160; </div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;    scramble_FFT(a, m);</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;    compute_1D_Butterfly&lt;FFT_REVERSE&gt;(a, m, log_len);</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160; </div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;    <span class="comment">//Do the scaling after ifft</span></div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    <span class="keywordflow">for</span> (Index i = 0; i &lt; m; ++i) {</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;      a[i] /= m;</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    }</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160; </div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;    <span class="keywordflow">for</span> (Index i = 0; i &lt; n; ++i) {</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;      <span class="keywordflow">if</span>(FFTDir == FFT_FORWARD) {</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;        data[i] = a[i] * numext::conj(pos_j_base_powered[i]);</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;      }</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;      <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;        data[i] = a[i] * pos_j_base_powered[i];</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;      }</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;    }</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;  }</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160; </div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">static</span> <span class="keywordtype">void</span> scramble_FFT(ComplexScalar* data, Index n) {</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;    eigen_assert(isPowerOfTwo(n));</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 1;</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;    <span class="keywordflow">for</span> (Index i = 1; i &lt; n; ++i){</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;      <span class="keywordflow">if</span> (j &gt; i) {</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;        std::swap(data[j-1], data[i-1]);</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;      }</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;      <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = n &gt;&gt; 1;</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;      <span class="keywordflow">while</span> (m &gt;= 2 &amp;&amp; j &gt; m) {</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;        j -= m;</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;        m &gt;&gt;= 1;</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;      }</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;      j += m;</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;    }</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;  }</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160; </div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;  <span class="keyword">template</span> &lt;<span class="keywordtype">int</span> Dir&gt;</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> butterfly_2(ComplexScalar* data) {</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;    ComplexScalar tmp = data[1];</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;    data[1] = data[0] - data[1];</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;    data[0] += tmp;</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;  }</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160; </div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;  <span class="keyword">template</span> &lt;<span class="keywordtype">int</span> Dir&gt;</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> butterfly_4(ComplexScalar* data) {</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    ComplexScalar tmp[4];</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;    tmp[0] = data[0] + data[1];</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    tmp[1] = data[0] - data[1];</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    tmp[2] = data[2] + data[3];</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    <span class="keywordflow">if</span> (Dir == FFT_FORWARD) {</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;      tmp[3] = ComplexScalar(0.0, -1.0) * (data[2] - data[3]);</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;    } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;      tmp[3] = ComplexScalar(0.0, 1.0) * (data[2] - data[3]);</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    }</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;    data[0] = tmp[0] + tmp[2];</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;    data[1] = tmp[1] + tmp[3];</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;    data[2] = tmp[0] - tmp[2];</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;    data[3] = tmp[1] - tmp[3];</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;  }</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160; </div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;  <span class="keyword">template</span> &lt;<span class="keywordtype">int</span> Dir&gt;</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> butterfly_8(ComplexScalar* data) {</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;    ComplexScalar tmp_1[8];</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;    ComplexScalar tmp_2[8];</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160; </div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;    tmp_1[0] = data[0] + data[1];</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;    tmp_1[1] = data[0] - data[1];</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;    tmp_1[2] = data[2] + data[3];</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;    <span class="keywordflow">if</span> (Dir == FFT_FORWARD) {</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;      tmp_1[3] = (data[2] - data[3]) * ComplexScalar(0, -1);</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;    } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;      tmp_1[3] = (data[2] - data[3]) * ComplexScalar(0, 1);</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    }</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;    tmp_1[4] = data[4] + data[5];</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;    tmp_1[5] = data[4] - data[5];</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;    tmp_1[6] = data[6] + data[7];</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;    <span class="keywordflow">if</span> (Dir == FFT_FORWARD) {</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;      tmp_1[7] = (data[6] - data[7]) * ComplexScalar(0, -1);</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;    } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;      tmp_1[7] = (data[6] - data[7]) * ComplexScalar(0, 1);</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;    }</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;    tmp_2[0] = tmp_1[0] + tmp_1[2];</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;    tmp_2[1] = tmp_1[1] + tmp_1[3];</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;    tmp_2[2] = tmp_1[0] - tmp_1[2];</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;    tmp_2[3] = tmp_1[1] - tmp_1[3];</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;    tmp_2[4] = tmp_1[4] + tmp_1[6];</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;<span class="comment">// SQRT2DIV2 = sqrt(2)/2</span></div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;<span class="preprocessor">#define SQRT2DIV2 0.7071067811865476</span></div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    <span class="keywordflow">if</span> (Dir == FFT_FORWARD) {</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;      tmp_2[5] = (tmp_1[5] + tmp_1[7]) * ComplexScalar(SQRT2DIV2, -SQRT2DIV2);</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;      tmp_2[6] = (tmp_1[4] - tmp_1[6]) * ComplexScalar(0, -1);</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;      tmp_2[7] = (tmp_1[5] - tmp_1[7]) * ComplexScalar(-SQRT2DIV2, -SQRT2DIV2);</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;    } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;      tmp_2[5] = (tmp_1[5] + tmp_1[7]) * ComplexScalar(SQRT2DIV2, SQRT2DIV2);</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;      tmp_2[6] = (tmp_1[4] - tmp_1[6]) * ComplexScalar(0, 1);</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;      tmp_2[7] = (tmp_1[5] - tmp_1[7]) * ComplexScalar(-SQRT2DIV2, SQRT2DIV2);</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;    }</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;    data[0] = tmp_2[0] + tmp_2[4];</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;    data[1] = tmp_2[1] + tmp_2[5];</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;    data[2] = tmp_2[2] + tmp_2[6];</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;    data[3] = tmp_2[3] + tmp_2[7];</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;    data[4] = tmp_2[0] - tmp_2[4];</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;    data[5] = tmp_2[1] - tmp_2[5];</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;    data[6] = tmp_2[2] - tmp_2[6];</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;    data[7] = tmp_2[3] - tmp_2[7];</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;  }</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160; </div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;  <span class="keyword">template</span> &lt;<span class="keywordtype">int</span> Dir&gt;</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> butterfly_1D_merge(</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;      ComplexScalar* data, Index n, Index n_power_of_2) {</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;    <span class="comment">// Original code:</span></div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;    <span class="comment">// RealScalar wtemp = std::sin(M_PI/n);</span></div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;    <span class="comment">// RealScalar wpi =  -std::sin(2 * M_PI/n);</span></div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;    <span class="keyword">const</span> RealScalar wtemp = m_sin_PI_div_n_LUT[n_power_of_2];</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;    <span class="keyword">const</span> RealScalar wpi = (Dir == FFT_FORWARD)</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;                               ? m_minus_sin_2_PI_div_n_LUT[n_power_of_2]</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;                               : -m_minus_sin_2_PI_div_n_LUT[n_power_of_2];</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160; </div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;    <span class="keyword">const</span> ComplexScalar wp(wtemp, wpi);</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;    <span class="keyword">const</span> ComplexScalar wp_one = wp + ComplexScalar(1, 0);</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;    <span class="keyword">const</span> ComplexScalar wp_one_2 = wp_one * wp_one;</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;    <span class="keyword">const</span> ComplexScalar wp_one_3 = wp_one_2 * wp_one;</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;    <span class="keyword">const</span> ComplexScalar wp_one_4 = wp_one_3 * wp_one;</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;    <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n2 = n / 2;</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;    ComplexScalar w(1.0, 0.0);</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;    <span class="keywordflow">for</span> (Index i = 0; i &lt; n2; i += 4) {</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;       ComplexScalar temp0(data[i + n2] * w);</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;       ComplexScalar temp1(data[i + 1 + n2] * w * wp_one);</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;       ComplexScalar temp2(data[i + 2 + n2] * w * wp_one_2);</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;       ComplexScalar temp3(data[i + 3 + n2] * w * wp_one_3);</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;       w = w * wp_one_4;</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160; </div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;       data[i + n2] = data[i] - temp0;</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;       data[i] += temp0;</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160; </div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;       data[i + 1 + n2] = data[i + 1] - temp1;</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;       data[i + 1] += temp1;</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160; </div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;       data[i + 2 + n2] = data[i + 2] - temp2;</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;       data[i + 2] += temp2;</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160; </div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;       data[i + 3 + n2] = data[i + 3] - temp3;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;       data[i + 3] += temp3;</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;    }</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;  }</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160; </div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160; <span class="keyword">template</span> &lt;<span class="keywordtype">int</span> Dir&gt;</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> compute_1D_Butterfly(</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;      ComplexScalar* data, Index n, Index n_power_of_2) {</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;    eigen_assert(isPowerOfTwo(n));</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;    <span class="keywordflow">if</span> (n &gt; 8) {</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;      compute_1D_Butterfly&lt;Dir&gt;(data, n / 2, n_power_of_2 - 1);</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;      compute_1D_Butterfly&lt;Dir&gt;(data + n / 2, n / 2, n_power_of_2 - 1);</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;      butterfly_1D_merge&lt;Dir&gt;(data, n, n_power_of_2);</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (n == 8) {</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;      butterfly_8&lt;Dir&gt;(data);</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (n == 4) {</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;      butterfly_4&lt;Dir&gt;(data);</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (n == 2) {</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;      butterfly_2&lt;Dir&gt;(data);</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;    }</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;  }</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160; </div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> getBaseOffsetFromIndex(Index index, Index omitted_dim)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> result = 0;</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160; </div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;    <span class="keywordflow">if</span> (<span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(Layout) == <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="codeRef" href="../group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a>)) {</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = NumDims - 1; i &gt; omitted_dim; --i) {</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> partial_m_stride = m_strides[i] / m_dimensions[omitted_dim];</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> idx = index / partial_m_stride;</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;        index -= idx * partial_m_stride;</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;        result += idx * m_strides[i];</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;      }</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;      result += index;</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;    }</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;    <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;      <span class="keywordflow">for</span> (Index i = 0; i &lt; omitted_dim; ++i) {</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> partial_m_stride = m_strides[i] / m_dimensions[omitted_dim];</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> idx = index / partial_m_stride;</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;        index -= idx * partial_m_stride;</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;        result += idx * m_strides[i];</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;      }</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;      result += index;</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;    }</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;    <span class="comment">// Value of index_coords[omitted_dim] is not determined to this step</span></div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;    <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;  }</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160; </div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> getIndexFromOffset(Index base, Index omitted_dim, Index offset)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> result = base + offset * m_strides[omitted_dim] ;</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;    <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;  }</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160; </div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160; <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;  <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m_size;</div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;  <span class="keyword">const</span> FFT EIGEN_DEVICE_REF m_fft;</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;  Dimensions m_dimensions;</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;  array&lt;Index, NumDims&gt; m_strides;</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;  TensorEvaluator&lt;ArgType, Device&gt; m_impl;</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  EvaluatorPointerType m_data;</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;  <span class="keyword">const</span> Device EIGEN_DEVICE_REF m_device;</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160; </div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;  <span class="comment">// This will support a maximum FFT size of 2^32 for each dimension</span></div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;  <span class="comment">// m_sin_PI_div_n_LUT[i] = (-2) * std::sin(M_PI / std::pow(2,i)) ^ 2;</span></div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;  <span class="keyword">const</span> RealScalar m_sin_PI_div_n_LUT[32] = {</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;    RealScalar(0.0),</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;    RealScalar(-2),</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;    RealScalar(-0.999999999999999),</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;    RealScalar(-0.292893218813453),</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;    RealScalar(-0.0761204674887130),</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;    RealScalar(-0.0192147195967696),</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;    RealScalar(-0.00481527332780311),</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;    RealScalar(-0.00120454379482761),</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;    RealScalar(-3.01181303795779e-04),</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;    RealScalar(-7.52981608554592e-05),</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;    RealScalar(-1.88247173988574e-05),</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;    RealScalar(-4.70619042382852e-06),</div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;    RealScalar(-1.17654829809007e-06),</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;    RealScalar(-2.94137117780840e-07),</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;    RealScalar(-7.35342821488550e-08),</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;    RealScalar(-1.83835707061916e-08),</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;    RealScalar(-4.59589268710903e-09),</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;    RealScalar(-1.14897317243732e-09),</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;    RealScalar(-2.87243293150586e-10),</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;    RealScalar( -7.18108232902250e-11),</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;    RealScalar(-1.79527058227174e-11),</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;    RealScalar(-4.48817645568941e-12),</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;    RealScalar(-1.12204411392298e-12),</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;    RealScalar(-2.80511028480785e-13),</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;    RealScalar(-7.01277571201985e-14),</div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;    RealScalar(-1.75319392800498e-14),</div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;    RealScalar(-4.38298482001247e-15),</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;    RealScalar(-1.09574620500312e-15),</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;    RealScalar(-2.73936551250781e-16),</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;    RealScalar(-6.84841378126949e-17),</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;    RealScalar(-1.71210344531737e-17),</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;    RealScalar(-4.28025861329343e-18)</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;  };</div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160; </div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;  <span class="comment">// m_minus_sin_2_PI_div_n_LUT[i] = -std::sin(2 * M_PI / std::pow(2,i));</span></div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;  <span class="keyword">const</span> RealScalar m_minus_sin_2_PI_div_n_LUT[32] = {</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;    RealScalar(0.0),</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;    RealScalar(0.0),</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;    RealScalar(-1.00000000000000e+00),</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;    RealScalar(-7.07106781186547e-01),</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;    RealScalar(-3.82683432365090e-01),</div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;    RealScalar(-1.95090322016128e-01),</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;    RealScalar(-9.80171403295606e-02),</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;    RealScalar(-4.90676743274180e-02),</div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;    RealScalar(-2.45412285229123e-02),</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;    RealScalar(-1.22715382857199e-02),</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;    RealScalar(-6.13588464915448e-03),</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;    RealScalar(-3.06795676296598e-03),</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;    RealScalar(-1.53398018628477e-03),</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;    RealScalar(-7.66990318742704e-04),</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;    RealScalar(-3.83495187571396e-04),</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;    RealScalar(-1.91747597310703e-04),</div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;    RealScalar(-9.58737990959773e-05),</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;    RealScalar(-4.79368996030669e-05),</div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;    RealScalar(-2.39684498084182e-05),</div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;    RealScalar(-1.19842249050697e-05),</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;    RealScalar(-5.99211245264243e-06),</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;    RealScalar(-2.99605622633466e-06),</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;    RealScalar(-1.49802811316901e-06),</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;    RealScalar(-7.49014056584716e-07),</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;    RealScalar(-3.74507028292384e-07),</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;    RealScalar(-1.87253514146195e-07),</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;    RealScalar(-9.36267570730981e-08),</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;    RealScalar(-4.68133785365491e-08),</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;    RealScalar(-2.34066892682746e-08),</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;    RealScalar(-1.17033446341373e-08),</div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;    RealScalar(-5.85167231706864e-09),</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;    RealScalar(-2.92583615853432e-09)</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;  };</div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;};</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160; </div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;}  <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160; </div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// EIGEN_CXX11_TENSOR_TENSOR_FFT_H</span></div>
<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62"><div class="ttname"><a href="../group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">Eigen::ColMajor</a></div><div class="ttdeci">ColMajor</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div></div>
<div class="ttc" id="anamespaceEigen_html_aa539408a09481d35961e11ee78793db1"><div class="ttname"><a href="../namespaceEigen.html#aa539408a09481d35961e11ee78793db1">Eigen::arg</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_arg_op&lt; typename Derived::Scalar &gt;, const Derived &gt; arg(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="../structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div></div>
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